Speaker
Dr
Jesse Stryker
(University of Washington)
Description
Motivated by the limited capabilities of near-term quantum computers,
we reconsider the Hamiltonian formulation of lattice gauge theories
and the method of truncating Hilbert space to render it
finite-dimensional. Conventional formulations lead to a Hilbert space
largely spanned by unphysical states; given the current inability to
perform fault-tolerant large scale quantum computations, we examine
here how one might restrict wave function evolution entirely or mostly
to the physical subspace. We consider such constructions for the
simplest of these theories containing dynamical gauge bosons — $U(1)$
lattice gauge theory without matter in d = 2, 3 spatial dimensions —
and find that electric-magnetic duality naturally plays an important
role. We conclude that this approach is likely to significantly reduce
computational overhead in d = 2 by a reduction of variables. We
further investigate potential advantages of regulating magnetic
fluctuations in asymptotically-free theories, instead of electric
fluctuations, which have been the focus of previous truncation
proposals.